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If a1,a2,a3, ,an are in A.P. with common...

If `a_1,a_2,a_3, ,a_n` are in A.P. with common difference `d(w h e r ed!=0)`, then the sum of series. `sind (coseca_1 coseca_2+coseca_2 coseca_3 +....+ coseca_(n-1) cos e ca_n)` is equal to `cot a_1-cot a_n`

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If a_1,a_2,a_3,--- ,a_n are in A.P with common difference d (where d!=0 ) , then the sum of series. sind(cos e ca_1cos e ca_2+cos e ca_2cos e ca_3+ --+cos e ca_(n-1)cos e ca_n) is equal to cota_1-cota_n

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. If theta1,theta2,theta3, ,thetan are in AP, whose common difference ...

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  2. If (m+1) term of an A.P. is twice the(n+1) th term, prove that (3m+1) ...

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  3. If a1,a2,a3, ,an are in A.P. with common difference d(w h e r ed!=0), ...

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  4. If an A.P. is such that (a4)/(a7)=2/7, find (a6)/(a8) .

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  5. The 4th term of an A.P. is three times the first and the 7th term e...

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  6. Find the number of terms common to the two AP's 3,7,11,15.... 407 and...

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  7. the sum of terms equidistant from the beginning and end in an A...

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  8. If a1,a2,a3, ,an are an A.P. of non-zero terms, prove that 1/(a1a2)+...

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  9. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/...

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  10. The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that t...

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  11. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  12. Let Sn be the sum of first n terms of an A.P. with non-zero common d...

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  13. If there are (2n+1) terms in A.P., then prove that the ratio of the su...

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  14. The ratio of the sum of n terms of two A.P. s is (7n+1):(4n+27) . Fin...

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  15. Show that x^2+x y+y^2,z^2+xz+x^2, y^2+y z+z^2, are consecutive terms o...

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  16. If a ,b ,c are in A.P., prove that: i.(a-c)^2=4(a-b)(b-c) ii.a^2+c^2...

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  17. Find the sum of all those integers between 100 and 800 each of which o...

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  18. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  19. Suppose x and y are two real numbers such that the rth mean between xa...

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  20. The sum of two numbers is (13)/6dot An even number of arithmetic means...

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